I'm not sure how important traceability of sub-assemblies in the T&E environment. I have not done a QS-TE and am not up on the TE Suppliment.
I just finished an ISO 9K2K registration audit of an equipment manufacturer. To them, tracking sub-assemblies was not important. They didn't do it. The question was, what value? For example, if a controller goes bad they had no way to 'easily' determine what controller went into what machine (box sealers).
What is a sub-assembly? Well, it depends. Just as you can use the word 'system' and say that a system is made up of sub-systems which is made up of smaller sub-systems (or, in the case of business systems, processes). At some point you sorta get lost. This is because of the perspective issue. How you define something depends upon how and from where you are observing.
At the 'top' level, there is the turn-key who brings a number machines together into a line. Bump down a level and there is the equipment manufacturer. At that level the product is a machine - a 'black box' system. The next level would be things like controllers and action elements ('immediate sub-systems). They in turn are made up of smaller sub-systems. Sooner or later you reach the component level.
All this said, you have to determine within your company what you internally consider 'sub-assemblies'. For some products it's clearer than others. In the ISO example above, the company (and again, this is 'equipment', not tooling) assembles their controllers, among other 'sub-assemblies'. They do not track components to lots per se. That is, they could not tell you what components from what lot went into what controller. In a round about way one could 'approximate' what went into what by date, receivers and such but it would be a good guess, not a sure thing. The important part here is that it didn't matter. If you reviewed their nonconformance system there was no evidence that component failures were a problem. Controller failure was rare until you reached a certain age - like 4 or 5 years or something like that. Even after that, failure rates were very low.
The tracking of the controllers (sub-assemblies) was by a traveler. They used Mapix (an ERP software 'solution') for orders and part of the output was the 'traveler' for the sub-assembly. When it hit the 'main machine' for installation, all that paperwork (completed traveler, etc) went into the main folder for the machine.
I probably agree with your plant manager. But - your nonconformance system data should be analyzed to ensure you know what is and is not a problem. Then make a reasoned determination of whether traceability makes sense.
All this is written assuming that traceability is not a customer requirement or 'industry standard' (such as in explosives and aerospace / marine industries).